Real-time Error Control for Surgical Simulation

Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations.Comment: 12 pages, 16 figures, change of the title, submitted to IEEE TBM

A generic topological framework for physical simulation

This paper presents the use of a topological model to simulate a soft body deformation based on a Mass-Spring System. We provide a generic framework which can integrate any kind of geometrical meshes (hexahedral or tetrahedral elements), using several numerical integration schemes (Euler semi-implicit or implicit). This framework naturally allows topological changes in the simulated object during the animation. Our model is based on the 3D Linear Cell Complex topological model (itself based on a 3D combinatorial map), adding the extra information required for simulation purposes. Moreover, we present some adaptations performed on this data structure to fit our simulation requirements, and to allow efficient cutting or piercing in a 3D object

Real-time Biomechanical Modeling for Intraoperative Soft Tissue Registration

Computer assisted surgery systems intraoperatively support the surgeon by providing information on the location of hidden risk and target structures during surgery. However, soft tissue deformations make intraoperative registration (and thus intraoperative navigation) difficult. In this work, a novel, biomechanics based approach for real-time soft tissue registration from sparse intraoperative sensor data such as stereo endoscopic images is presented to overcome this problem